{
 "cells": [
  {
   "cell_type": "markdown",
   "id": "73bd968b-d970-4a05-94ef-4e7abf990827",
   "metadata": {},
   "source": [
    "Chapter 09\n",
    "\n",
    "# 正交投影\n",
    "Book_4《矩阵力量》 | 鸢尾花书：从加减乘除到机器学习 (第二版)"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "5cf69650-7deb-4770-a8ff-af8a2b7c34a3",
   "metadata": {},
   "source": [
    "这段代码展示了一个二维向量 $$x = \\begin{bmatrix} 4 \\\\ 3 \\end{bmatrix}$$\n",
    "在不同方向上投影的效果。首先，定义了从 0 到 \\( \\pi \\) 的 25 个角度构成的数组 `thetas`。对每个角度 \\(\\theta\\)，代码构造一个单位向量 \\( v(\\theta) \\)：\n",
    "\n",
    "$$\n",
    "v(\\theta) = \\begin{bmatrix} \\cos(\\theta) \\\\ \\sin(\\theta) \\end{bmatrix}\n",
    "$$\n",
    "\n",
    "该单位向量表示在平面上旋转的不同方向。然后，通过计算 \\( x \\) 在 \\( v \\) 上的投影：\n",
    "\n",
    "$$\n",
    "\\text{proj} = v^T \\cdot x\n",
    "$$\n",
    "\n",
    "得出 \\( x \\) 在每个 \\( v \\) 方向上的投影长度。代码将此投影结果可视化：首先绘制 \\( v \\) 方向的直线以指示投影方向，然后绘制从 \\( x \\) 到其投影点的线段，直观地展示出 \\( x \\) 在该方向上的投影点。最终效果展示了 \\( x \\) 随不同方向投影的变化，通过一个红色“x”标记出原始向量 \\( x \\) 的位置，并在各个方向上绘制投影，给出了 \\( x \\) 在旋转方向上不同投影的几何图形。"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "id": "4e72ef2c-b83d-48cb-b550-ca78fcdf48df",
   "metadata": {
    "tags": []
   },
   "outputs": [],
   "source": [
    "import numpy as np  # 导入数值计算库\n",
    "import matplotlib.pyplot as plt  # 导入绘图库\n",
    "from matplotlib.colors import hsv_to_rgb  # 导入HSV到RGB颜色转换函数"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "d5067145-7b42-4557-a522-8d57feb204de",
   "metadata": {
    "tags": []
   },
   "source": [
    "## 定义角度序列"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "id": "125df454-8366-4a70-b8de-fa48dd40a0a7",
   "metadata": {
    "tags": []
   },
   "outputs": [],
   "source": [
    "thetas = np.linspace(0, np.pi, 25)  # 生成从 0 到 π 的 25 个角度"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "27fc5f7d-99ff-4588-b592-647b0d196402",
   "metadata": {
    "tags": []
   },
   "source": [
    "## 定义向量 x"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "id": "84a7bf67-08d5-4516-bb23-3d6b794e2aa9",
   "metadata": {
    "tags": []
   },
   "outputs": [],
   "source": [
    "x = np.array([4, 3])  # 定义二维向量 x"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "500a0713-6fce-4265-a213-682d3502fe1b",
   "metadata": {
    "tags": []
   },
   "source": [
    "## 创建绘图子图"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "id": "04cc39a7-fcc8-4abc-9b27-4f6558eb8d4f",
   "metadata": {
    "tags": []
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "(-6.6, 6.6, -6.6, 6.6)"
      ]
     },
     "execution_count": 4,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "fig, ax = plt.subplots()  # 创建绘图子图\n",
    "\n",
    "## 投影计算和绘图\n",
    "for i, theta in enumerate(thetas):  # 遍历每个角度 theta\n",
    "    v = np.array([np.cos(theta), np.sin(theta)])  # 计算单位向量 v\n",
    "    \n",
    "    proj = np.dot(v, x)  # 计算 x 在 v 上的投影长度\n",
    "\n",
    "    # 根据角度映射颜色 (HSV 色谱)\n",
    "    hue = theta / np.pi  # 将角度归一化到 [0, 1]\n",
    "    color = hsv_to_rgb([hue, 1, 1])  # 转换为 RGB 颜色\n",
    "\n",
    "    # 绘制投影方向上的直线\n",
    "    ax.plot([-v[0]*6, v[0]*6], [-v[1]*6, v[1]*6], color=color)\n",
    "    \n",
    "    # 绘制 x 到投影点的线段\n",
    "    proj_point = proj * v  # 投影点坐标\n",
    "    ax.plot([x[0], proj_point[0]], [x[1], proj_point[1]], color=color, linestyle='-')\n",
    "    \n",
    "    # 绘制投影点\n",
    "    ax.plot(proj_point[0], proj_point[1], color=color, marker='x')\n",
    "\n",
    "    # 绘制单位向量 v\n",
    "    ax.quiver(0, 0, v[0], v[1], angles='xy', scale_units='xy', scale=1, color=color)\n",
    "\n",
    "## 绘制向量 x 的位置\n",
    "ax.plot(x[0], x[1], marker='x', color='r', label='Vector x')  # 绘制向量 x 的起点\n",
    "ax.axhline(y = 0, color = 'k')\n",
    "ax.axvline(x = 0, color = 'k')\n",
    "## 设置坐标轴比例\n",
    "ax.set_aspect('equal', 'box')\n",
    "ax.axis(False)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "id": "85a80909-2aac-49ed-bb7a-f8cc6b80ee7d",
   "metadata": {},
   "outputs": [],
   "source": []
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "id": "ecd322f4-f919-4be2-adc3-69d28ef25e69",
   "metadata": {},
   "outputs": [],
   "source": []
  }
 ],
 "metadata": {
  "kernelspec": {
   "display_name": "Python 3 (ipykernel)",
   "language": "python",
   "name": "python3"
  },
  "language_info": {
   "codemirror_mode": {
    "name": "ipython",
    "version": 3
   },
   "file_extension": ".py",
   "mimetype": "text/x-python",
   "name": "python",
   "nbconvert_exporter": "python",
   "pygments_lexer": "ipython3",
   "version": "3.12.7"
  }
 },
 "nbformat": 4,
 "nbformat_minor": 5
}
